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Multiplication of Matrices

if X sin ∧ 3 ...

Question

if X sin^3A + Y cos^3A = (sinA)(cosA) and X sinA = Y cosA , prove that X^2 + Y^2 = 1

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Solution

We know
XsinA=YcosA....(1)
and
Xsin³A+Ycos³A=sinAcosA
or
XsinA×sin²A+Ycos³A=sinAcosA
substituting....(1)
we get,
YcosA×sin²A+Ycos³A=sinAcosA
YcosA(sin²A+cos²A)= sinAcosA
i.e. Ycos A=sinAcosA (sin²A+cos²A=1)
so Y=sinA....(3)
substituting (3) in (1)
XsinA=sinAcosA
so X=cosA....(4)

X²+Y²=sin²A+cos²A=1
so
X²+Y²=1
Hence proved.

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